1、08FTM12AGMA Technical PaperIn-situ Measurement ofStresses in CarburizedGears via NeutronDiffractionBy R.A. LeMaster, B.L. Boggs,J.R. Bunn, and J.V. Kolwyck,University of Tennessee at Martinand C.R. Hubbard and W.B.Bailey, Oak Ridge NationalLaboratoryIn-situ Measurement of Stresses in Carburized Gear
2、s viaNeutron DiffractionR.A. LeMaster, B.L. Boggs, J.R. Bunn, and J.V. Kolwyck, University of Tennessee atMartin and C.R. Hubbard and W.B. Bailey, Oak Ridge National LaboratoryThe statements and opinions contained herein are those of the author and should not be construed as anofficial action or opi
3、nion of the American Gear Manufacturers Association.AbstractThetotalstressesinamatinggearpairarisefromtwosources:1)externallyinducedstressesassociatedwiththe transmission of power, and 2) residual stresses associated with the heattreatment and machining ofthetoothprofiles. Thestressesduetopowertrans
4、missionaretheresultofcomplexnormalandshearingforcesthatdevelopduringthemeshingsequence. Thetotalstressfromthesetwosourcescontributestothelifeofagear.Thispaperpresentstheresultsofresearchdirectedatmeasuringthetotalstressinapairofstaticallyloadedandcarburizedspurgears. Measurementsweremadeto examineth
5、echangeintotalstressasafunctionofexternallyappliedloadanddepthbelowthesurface. ThemeasurementsweremadeusingthenewNeutronResidual Stress Mapping Facility (NRSF2) instrument at Oak Ridge National Laboratory. A Static LoadApplication Device (SLAD) was developed to load the gear pair while mounted on th
6、e NRSF2 instrument.Neutron diffraction methods are non-destructive and involve measuring the inter-atomic spacing(d-spacing)ofatomsinthecrystallatticeusingdiffractometersthatmeasurethepositionofadiffractionpeak.The measured position is converted to d-spacing using Braggs Law. The change in d-spacing
7、 betweenstressed and unstressed states allows the determination of strains and consequently the stresses.Computation of strains using neutron diffraction methods requires that the lattice spacing in the strain-freecondition (d0) be known. The determination of d0for a carburized material is nottrivia
8、l due to carbon,phaseandmicrostructuregradientsthatexistnearthesurface. Thesegradientsrequirethatadifferentvalueofd0beknown at each measurement location. The paper includes a summary of various methods that are used todetermined0andadiscussionoftheirapplicabilitytocarburizedgears. Thepossibilityofde
9、terminingd0using-tiltmethodsisdiscussedandresultsarepresentedford0variationthroughthecarburizedlayerdeterminedusing the sin2 method.Copyright 2008American Gear Manufacturers Association500 Montgomery Street, Suite 350Alexandria, Virginia, 22314October, 2008ISBN: 978-1-55589-942-43In-situ Measurement
10、 of Stresses in Carburized Gears via Neutron DiffractionR.A. LeMaster, B.L. Boggs, J.R. Bunn, and J.V. Kolwyck, University of Tennessee atMartin, and C.R. Hubbard and W.B. Bailey, Oak Ridge National LaboratoryIntroductionThetotalstressinanoperatinggeariscomprisedoftwo types: 1) externally induced st
11、resses associat-ed with the transmission of power, and 2) residualstresses associated with the heat treatment andmachining of the tooth profiles. It is the combinedeffect of these two stress types that contributes tothe life of a gear.Stresses in metallic components can be measuredusing X-ray and ne
12、utron diffraction methods. His-torically, these methods have been used tomeasureonlyresidualstresses. X-rayandneutrondiffraction methods involve measuring the inter-planar spacing (d-spacing) of atoms in the crystallattice using diffractometers that measure the posi-tion of the diffraction maxima wh
13、ich is converted tod-spacing using Braggs Law. The measured d-spacing is the average value for a group of grainssuitablyorientedwithinanirradiatedsurfaceareaorvolume. The change in d-spacing betweenstressed and unstressed states allows thedeterminationofstrainsandconsequentlystresses.In recent years
14、 there has been interest in usingneutron diffraction methods to measure the in-situstresses in operatingequipment. It ishypothesizedthatthepenetratingfeatureofneutronswillallowthemeasurementofoperatingstressesinsidemechan-ical components something that would be totallyimpossible by X-ray methods. A
15、specific goal ofthis research was to determine the degree to whichneutron diffractioncan beused tomeasure thetotalstress in meshed carburized gears that are understatic load. Considering statically loaded butmeshed gears asa firststep wouldallow theeffectsof the near-surface chemistry, phases, and m
16、icro-structures to be isolated from dynamically inducedphenomena.Neutron diffractionNeutron diffraction is an experimental method usedto study the structure of a crystalline materials.Neutron diffraction instruments include a sourcecapable of generating a stream of neutrons calledabeam. This beam is
17、 directed at a sample and theintensity of the scattered neutrons is measured us-ing detectors. Variations of the intensity at differentangular positions around the sample provide infor-mation about the crystal structure of the sample.There are two primary types of neutron sources:1) nuclear reactors
18、 and 2) spallation sources. Theresearchpresentedinthisreportwasconductedus-ing the Neutron Residual Stress Facility (NRSF2)instrument that receives neutrons from the HighFluxIsotopeReactor(HIFR). HIFRislocatedattheOak Ridge National Laboratory in Oak Ridge, TN.Figure 1presents aschematic ofthe NRSF2
19、instru-ment that traces the neutron beam from the reactorto the six position sensitive detectors (PSDs). Thebeamleavingthereactorcorecontainsmanywave-lengthsandadeformableSicrystalmonochromatorisusedtoobtainoneofsixpossiblewavelengths. Awavelength of 1.54 Angstroms associated with theSi 422 plane wa
20、s used for most of this research.Figure 1. NRSF2 neutron beam schematicThesinglewavelengthbeamleavingthemonochro-mator passes through a snout containing slits. The4slits create a rectangular opening that control theincident beam width and height. The beam leavingthe slits passes through the sample t
21、hat diffracts afraction of the incident neutrons. When the beamencounters grains within the sample that have theirlattice planes oriented in a particular direction, thebeamwilldiffractandcauseapeakinthemeasuredintensity.The scattering angle at which the peak will occur isgoverned by Braggs Law: = 2d
22、 sin (1)where is the wavelength of the incident beammeasured in Angstroms, dis the lattice spacing be-tweentheatomsinthediffractingplanemeasuredinAngstroms, and is the diffraction angle (Figures 2and 3) in either degrees or radians. The d-spacingis obtained by rewriting equation 1 as:d =2sin(2)Thedi
23、ffractionangleisdetermined byfitting acurveto the detector intensity data. The location of thepeak intensity defines the diffraction angle. Thewavelength of the radiation leaving the monochro-mator enables the calculation of the d-spacingusing equation 2.In-situ strain measurementStatic load applica
24、tion device (SLAD)A static load application device (SLAD) was de-signedtoholdandstaticallyloadthetwogearsusedin these experiments. SLAD was also designed tobe compatible with the NRSF2 instrument. TheSLAD contains two major sub-assemblies: 1) aloading fixture (Figures 2a and 2b) and 2) a pumpsub-ass
25、embly(Figure3). Thetwosub-assembliesare connected by a ten foot long hydraulic hose. Astatic torque is applied to the test gear using ahydraulic cylinder. This torque is transferred fromthetestgeartoamatinggear thatis preventedfromrotatingbyasingletoothrack. Theorientationofthetest gear in the SLAD
26、was designed such that theprincipal direction of the bending stress at the criti-cal cross section was horizontal. This enabled thealignment of SLAD with the incident and diffractedbeams that also lie in the horizontal plane. Thegearsarealsopositionedsuchthatthecontactpointis at the worst load radiu
27、s.Figure 2a. SLAD load fixture showing the twomating gearsFigure 2b. CAD rendering of SLAD showingthe hydraulic cylinder and torque arm used toload the gearsFigure 3. Manually operating hydraulic pumpused to load gears (Plastic container is for spillcontainment)5SLAD was designed to induce a 140 ksi
28、 bendingstress at the critical cross section in the fillet regionof the tooth. Using the equations at the bottom ofTable1itwasdeterminedthatthisstressoccursatahydraulic cylinder pressure of approximately 1,400psi. The bending stress and associated strain foreachofthepressuresusedinthetestsareshownin
29、Table 1. The 140 ksi maximum stress level waschosenbecause thecompressive residualstressesofthismagnitude,whichweremeasuredonthesur-face of the gears using x-ray diffraction 1, wouldbe approximately balanced out and the resultingstress would be near zero.Experimental setupThe experiment was designed
30、 to measure d-spacing in three orthogonal directions using theSLAD and NRSF2 instrument. The measurementofd-spacinginthreeorthogonal directionsrequiredmounting the SLAD on the NRSF2 instrument inthree orientations. The first orientation waschosento measure the d-spacing for the longitudinal strainco
31、mponent at the location of the critical bendingstress in the fillet area. A 3 0.3 3 mm slitarrangement was used. The second orientationwas achieved by rotating the -axis of the NRSF2instrument by 90 degrees. This orientation wasused to measure the d-spacing forthe lateralstraincomponent at the criti
32、cal bending stress location.Thesame slitarrangement wasused. The thirdori-entation was orthogonal to the first two orientationsand was achieved by physically rotating the SLADby 90 degrees. This orientation was used to mea-surethed-spacingforthenormalstraincomponentat the bending stress location. A
33、“hanging slit” con-figuration was required with the lateral and normaldirections to avoid interference issues between theNRSF2 instrument and the SLAD.The d-spacing measurements were taken at ninedepths (0.08, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50,1.75, and 2.00 mm) in each orientation and at sixhydrau
34、lic cylinder pressures of approximately 100,360, 620, 880, 1140, and 1400 psi. The actualpressures used in each orientation were slightlydifferent due to the inability to achieve a precisepressure using the manually operated pump.Experimental dataMeasured d-spacing for the longitudinal, lateral,and
35、normal directions at various pressures anddepths are summarized in Tables 2, 3, and 4. All ofthe measurements were taken near the center ofthe tooth (8.5 mm in from the side of the gear).Figures 4, 5, and 6 show all of the d-spacing for aparticular direction versus depth on a single graph.SLAD data
36、analysisTheeffectofincreasingthetoothloadbyanexternalsourceond-spacingforthelongitudinalstraincom-ponentisclearlyseeninFigure4. Atthelowestloadlevel(116psi cylinderpressure) thepresence ofthecompressive residual stress state is evident. Thed-spacing is smallest near the surface where thecompressive
37、residual stress is highest. The d-spacing increases as the measurement depth in-side the carburized layer increases. This corre-sponds to a decreasing compressive stress statewith increasing distance from the surface. As thetooth load is increased the d-spacing increaseswhich is expected from the co
38、mbination of a com-pressive residual stress and tensile stress resultingfrom the external load.Table 1. Critical bending stress and strainCylinder pressure,psiTorque, in-lb Transverse toothforce, Wt,lbPeak bendingstress, bPeak bendingstrain, b116 2,640 845 11.9 410340 7,740 2,480 34.8 1,200625 14,20
39、0 4,540 63.7 2,200883 20,100 6,430 90.2 3,1101,136 25,900 8,290 116.0 4,0001,387 31,600 10,100 142.0 4,900b=WtPdFJJ =0.38F =0.75in;Pd= 4 teeth/inE =29 106psib=bE6Table 2. d-spacing for longitudinal strain component versus measurement depth and hydrauliccylinder pressureDepthAverage pressure, psi116.
40、 340. 625. 883. 1136. 1387.d-spacing (A)0.08 1.16925 1.17093 1.17111 1.17231 1.17246 1.172800.25 1.16997 1.17040 1.17228 1.17245 1.17320 1.172980.50 1.17052 1.17157 1.17190 1.17272 1.17273 1.172870.75 1.17081 1.17182 1.17262 1.17239 1.17256 1.172891.00 1.17106 1.17193 1.17196 1.17249 1.17251 1.17299
41、1.25 1.17113 1.17196 1.17223 1.17251 1.17298 1.172971.50 1.17138 1.17181 1.17211 1.17257 1.17280 1.172781.75 1.17156 1.17192 1.17218 1.17249 1.17279 1.172832.00 1.17169 1.17218 1.17225 1.17252 1.17233 1.17271Table 3. d-spacing for lateral strain component versus measurement depth and hydrauliccylind
42、er pressureDepthAverage pressure, psi119. 363. 619. 894. 1125. 1389.d-spacing (A)0.08 1.17063 1.17078 1.17097 1.17092 1.17118 1.171710.25 1.17118 1.17082 1.17102 1.17131 1.17103 1.171070.50 1.17132 1.17131 1.17105 1.17090 1.17085 1.171020.75 1.17132 1.17117 1.17112 1.17117 1.17101 1.171061.00 1.1714
43、5 1.17121 1.17136 1.17135 1.17134 1.171291.25 1.17140 1.17164 1.17164 1.17158 1.17154 1.171551.50 1.17182 1.17168 1.17171 1.17172 1.17168 1.171631.75 1.17169 1.17178 1.17166 1.17163 1.17163 1.171582.00 1.17170 1.17170 1.17163 1.17155 1.17160 1.17153Table 4. d-spacing for normal strain component vers
44、us measurement depth and hydrauliccylinder pressureDepthAverage pressure, psi104. 359. 614. 868. 1182. 1352.d-spacing (A)0.00 1.17264 1.16929 1.16903 1.16903 1.1927 1.169050.25 1.17195 1.16920 1.16900 1.16900 1.16953 1.168910.50 1.17196 1.16929 1.16899 1.16889 1.16947 1.169250.75 1.17205 1.16905 1.1
45、6892 1.16892 1.16941 1.169231.00 1.17178 1.16944 1.16903 1.16903 1.16975 1.169311.25 1.17178 1.16893 1.16921 1.16921 1.16955 1.169181.50 1.17185 1.16916 1.16925 1.16925 1.16969 1.169251.75 1.17146 1.16914 1.16935 1.16935 1.16957 1.169252.00 1.17183 1.16917 1.16943 1.16943 1.16958 1.169347Figure 4. V
46、ariation of d-spacing for the longitudinal strain component with depth at different testpressuresFigure 5. Variation of d-spacing for the lateral strain component with depth at different testpressures8Figure 6. Variation of d-spacing for the normal strain component with depth at different testpressu
47、resThe SLAD device was designed to create a totalstressofzero atthe criticalstress locationon thefil-let at a pressure of 1,400 psi. The data shown inFigure 4 suggests that this was accomplished. At116 psi the compressive d-spacing gradient isclearly seen. In contrast, at a hydraulic cylinderpressur
48、e of 1,387 psi the d-spacing gradient isnearly zero. The cancelling of the d-spacinggradient as the cylinder pressure is increased isconsistent with the compressive residual stress onthe surface of 140 ksi as measured using X-raydiffraction. It also shows that the AGMA toothbending equation given by
49、, =WtPtFJwhere Wtis the transverse component of thecontact force, Pdisthediametralpitch,Fis thefacewidth,andJisthebendinggeometryfactor(0.38forthe gears used in this test), gave accurate results.Further increases in hydraulic cylinder pressureresult in higher d-spacing on the surface.Theeffectofincreasingtoothloadonthed-spacingforthelateralstrain componentsis notpronounced.Thed-spacingdataforthelateraldirectionisnearlythesameforallpressuresandasinglelinecanbefitto all of the data (Figure 5). The measur
